Chapter 4, Problem 40
A 94.9-kg person stands on a scale in an elevator. What is the apparent weight when the elevator is (a) accelerating upward with an acceleration of 2.30 m/s^2, (b) moving upward at a constant speed, and (c) accelerating downward with an acceleration of 1.70 m/s^2?
a) m (9.8+2.3)
b) m (9.9 -1.7)
To find the apparent weight of the person in the elevator, we need to understand the forces acting on them. The apparent weight is the force exerted by the scale on the person, which is equal to the normal force.
(a) When the elevator is accelerating upward with an acceleration of 2.30 m/s^2:
In this case, the net force acting on the person is the sum of their weight (mg) and the force due to acceleration (ma). The equation that represents this is:
ΣF = ma + mg
The force due to acceleration is calculated as the mass of the person multiplied by the acceleration:
Force due to acceleration = ma = (94.9 kg)(2.30 m/s^2)
The weight of the person is the force due to gravity exerted on them and can be calculated as:
Weight = mg = (94.9 kg)(9.8 m/s^2)
To find the apparent weight, we need to find the normal force, which is equal to the sum of the weight and the force due to acceleration:
Apparent weight = weight + force due to acceleration
(b) When the elevator is moving upward at a constant speed:
When the elevator is moving at a constant speed, the net force acting on the person is zero. This means that the force due to acceleration is equal in magnitude and opposite in direction to the weight of the person. Thus, the apparent weight is equal to the person's actual weight.
(c) When the elevator is accelerating downward with an acceleration of 1.70 m/s^2:
In this case, the net force acting on the person is the difference between their weight and the force due to acceleration. The equation that represents this is:
ΣF = mg - ma
Similarly, we can calculate the force due to acceleration and the weight of the person, and then find the apparent weight by summing them:
Force due to acceleration = ma = (94.9 kg)(1.70 m/s^2)
Weight = mg = (94.9 kg)(9.8 m/s^2)
Apparent weight = weight - force due to acceleration
By using these equations and the given values, you can calculate the apparent weight of the person in each scenario.